AP Calculus AB/BC by Sourcebooks

145
Total Questions

2
Tests

150
Lessons

Overview

AP Calculus AB/BC by Sourcebooks offers strategies for maximizing your score on the AP Calculus exam. With 145 practice questions and 2 mini-tests, Sourcebooks' AP Calculus AB/BC prep course will help you along in every subject covered on the AP Calculus exam.

Topics Covered

Topics and Concepts Covered

Introduction

The Essentials: A Last-Minute Study Guide

THE ESSENTIALS: A LAST-MINUTE STUDY GUIDE

20 Problems You Must Be Able to Solve

20 Problems You Must Be Able to Solve

1. Area of the Region Between Two Curves

2. Area in Polar Form

3. Volume of Solid of Revolution

4. Volume by Cross Sections

5. Particle Motion

6. Particle Motion in Parametric or Vector Form

7. Particle Motion in Polar Form

8. Curve Sketching

9. Linear Approximation

10. Graphical Analysis

11. Analysis of Data

12. Differential Equations

13. Exponential Growth

14. Riemann Sums and Trapezoidal Rule

15. Implicit Differentiation

16. Average Value

17. Related Rates

18. Taylor Series and Error Bounds

19. Series and Intervals of Convergence

20. Critical Theorems

Strategies for Maximizing Your Score

How to Guess

How to Show Your Work

How to Show Your Work

1. Spell It Out

2. Keep Your House in Order

3. Show All Your Work

4. Don't Do a Brain Dump

5. Conserve Your Time

6. Use Your Calculator Wisely

7. Finish the Job

Checklist for Test Day

The Main Course: Comprehensive Strategies and Review

The Main Course: Comprehensive Strategies and Review

Topic 1: Limits

Topic 1: Limits

One-Sided Limits

DNE

Properties of Limits

Algebraic Techniques for Calculating Limits

The Squeeze Theorem

Memory Work

Limits at Infinity

Infinite Limits

Asymptotes

Continuity

L'Hopital's Rule

Topic 2: Derivatives

Topic 2: Derivatives

Difference Quotient

Derivative of a Function f at a Point

Derivative Function

Differentiability

Basic Derivatives

Memory Work

Implicit Differentiation

Higher Order Derivatives

Topic 3: Applications of the Derivative

Topic 3: Applications of the Derivative

Average Rate of Change

Instantaneous Rate of Change

Tangent Lines

Tangent Line Approximation

Local Linearization = First Degree Taylor Polynomial

Error of Estimate

Sign of the Error

Newton's Method

Particle Motion

Optimization

Related Rates

Normal Line

Rolle's Theorem and the Mean Value Theorem

Topic 4: Curve Sketching

Topic 4: Curve Sketching

First and Second Derivatives

Absolute Extrema

Vertical Asymptotes

Cusps

End Behavior

Topic 5: Integrals

Topic 5: Integrals

Riemann Sum

Trapezoidal Rule

Fundamental Theorem of Calculus

Basic Antiderivatives

U-Substitution

Improper Integrals

Topic 6: Parts and Partial Fractions

Topic 6: Parts and Partial Fractions

Integration by Parts

Partial Fraction Decomposition

Topic 7: Applications of the Integral

Topic 7: Applications of the Integral

Fundamental Theorem of Calculus

Area Under a Curve

Average Value

Length of a Curve

Distance Traveled and Displacement

Work

Topic 8: Area and Volume

Topic 8: Area and Volume

Area under a Curve

Area between Two Curves

Volume of a Solid of Revolution

Method of Discs

Method of Washers

Volume of a Solid by Cross Sections

Topic 9: Differential Equations

Topic 9: Differential Equations

Separable Differential Equations

Euler's Method

Slope Fields

Topic 10: Graphical and Numerical Presentations

Topic 11: Infinite Series

Topic 11: Infinite Series

Series Facts

Does the Series Converge?

Series to Remember

Radius and Interval of Convergence

Deriving Power Series from a Known Series

Deriving Series by Differentiation and Integration

Taylor Polynomial Approximations

Error of Approximation

Lagrange Error Bound

Topic 12: Parametric Equations and Vector Functions

Topic 12: Parametric Equations and Vector Functions

Parametric Equations

Vector Functions

Eliminating the Parameter

Magnitude of a Vector

Differentiation

Tangent Lines

Applications of the Derivative

Integration

Applications of the Integral

Area under a Curve

Topic 13: Polar Curves

Topic 13: Polar Curves

Basics

Conversion

Converting Equations

Polar Equations and Their Graphs

Tangents

Area

Arc Length

Formula Glossary

Trigonometry

Limits

Derivatives and Antiderivatives

Applications of the Derivative and the Integral

Differential Equations

Series

Vectors and Parametrics

Multiple Choice Strategies

Multiple Choice Strategies

Don't Find What You Don't Need

Don't Calculate When an Estimate Will Do

Understand the Relationship between the Graphs of'f, f', and'f''

Understand the Relationship between Distance, Velocity, and Acceleration

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